nothing worked until I performed that wget from IPfire. Is it coincidence or did that kick something within the system?

It seems extremely unlikely to me because I can't think of any mechanism that would trigger a behaviour like that. To rule it out (as it's always bad to assume things) is easy. Just restart the box.
If you could reproduce it reliably, it would qualify as an Ipfire bug IMO. If not, it's a mystery that can't be solved unfortunately.

nothing worked until I performed that wget from IPfire. Is it coincidence or did that kick something within the system?

It seems extremely unlikely to me because I can't think of any mechanism that would trigger a behaviour like that. To rule it out (as it's always bad to assume things) is easy. Just restart the box.
If you could reproduce it reliably, it would qualify as an Ipfire bug IMO. If not, it's a mystery that can't be solved unfortunately.

I just restarted my IPfire system to see what would happen. Everything still worked afterwards. I can access all sites just fine. No idea why this happened. The problem came out of nowhere, lasted for about a week, and then suddenly stopped. I know someone suggested that I might have been on a blacklist for some reason, but there were several sites that I could not access through a browser. I only posted the ones that were most important to me.

Well, I just upgraded to Core 135 and now the problem is back. Again, there lots of sites that will not load behind IPfire. If I use my VPN or if I connect directly to my cable modem, they load just fine. It’s not an IP issue or a blacklist issue. It has to be an IPfire issue. The problem seemed to go away until I upgraded to Core 135. This is becoming really aggravating.

Any ideas? This is driving me nuts. Why do some websites load fine while others won't load at all?

Edit: just to be clear, if I connect to my VPN, I can access these sites just fine. If I bypass IPfire and connect straight to the cable modem, I can access them just fine. If I turn off WiFi on my phone and just my carrier's data network, I can access them just fine. IPfire is the problem.

Update: the problem is back a few days after my rebuild. This time, the problem is slightly different. I can get to all my work websites that I was not able to reach before (the Mantech.com websites), but I am unable to log into my online school's web page, just like before. It just hangs and hangs until it times out. Again, this happens in all browsers on all computers. If I fire up my VPN, I can connect just fine. I even did a wget from IPfire and it looks like the connection is being established (see below), so why does this keep happening?? This is getting super aggravating. I shouldn't have to use a VPN to log into sites I need to access because IPfire stops working.

However, now I can no longer get to http://apps.webster.edu/compcen/datadic ... form2.php3 which I was able to get to this morning. It's like IPfire keeps rotating through which websites are allowed via http or https because it keeps changing. If this doesn't stop, I'm going to have to move away from IPfire.